PTG202

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Stressandstrain.pptx

Force, stress and strength

Dr. Said M Said 2020

Forces arising from plate interactions result in a range of geologic structures, from microfabrics to mountain ranges

To understand tectonic processes we must be familiar with the fundamental principles of mechanics Mechanics is concerned with the action of forces on bodies and their effect (science of Motion)

Force definition: is a vector quantity that tends to produce a change in the motion or the state of a body, or is the push or pull on an object with mass that causes it to change velocity (to accelerate). A force is defined by its magnitude and direction. F = m * a Where, “m” is the mass of the body, “a” is the acceleration of motion of the body. Its units is Newton. Newton is equal to 1 kg*m*s-2 .

Force

A single force can be resolved into two components:

Horizontal force (Fx= F sinθ )

Vertical force (Fy= F Cos θ)

Plate tectonic forces

Tectonic forces trigger acceleration of rock bodies that are at state of rest or slow motion

Forces have two scale of effect

1. unimaginably slow acceleration of the larger geologic unit as a whole, such as a major tectonic plate that undergoes an increase in velocity from 6 cm/yr to 7 cm/yr over hundreds or thousands of years; or

2.incredibly fast, short-lived accelerations of parts of the larger body, such as fault-induced shifting of rock in the briefest period of time (seconds or fractions of seconds), achieving huge accelerations

(Seismic events )

plate forces build

Slowely, until strength

of the crust is overcome,

this triggering internal

Adjustment by

distortion, 2. rotation

3. Translation or 4. dilation

Some of these effects are

Recoverable and some are

Not

TRACTIONS

Traction ( T) is a vector quantity that considers the magnitude of a force ( F) in relation to the area (A) of the surface on which it acts

T =

Units of traction pascal (pa) or Kpa or Kg/cm3 or N/m2

External and Internal Tractions

In static equilibrium, the tractions (Tdown, Tup) acting on a surface at a point in the body are equal in magnitude and oppositely directed

Surface stress at point

If the tractions of this surface stress act toward one another, the surface stress is compressive. Compression is considered to be positive (+)

Tractions can be resolved into normal components (σn) and shear components (σs) σn acts perpendicular to the surface on which the traction operates; σs acts parallel to that same surface

Determining Normal and Shear (Surface) Stresses on any Plane

A force vector F acting on a surface can be decomposed into a normal (Fn) and a shear (Fs) component by simple vector addition. The stress vectors cannot be decomposed in this way, because it depends on the area across which the force acts. Trigonometric expressions for the components σn and σs are derived.

Principal Stress Directions

stresses acting on vertical planes and horizontal planes are very special cases

Stress ellipse

shear stress is at its maximum at 45 to the surface while maximum shear force is obtained parallel to the surface

The long axis of the ellipse is referred to as the axis of greatest principal stress (σ1); the short axis is known as the axis of least principal stress (σ3).

In 3D dynamic analysis, it is the stress ellipsoid that provides the description of the stress tensor at a point. In addition to the axes of greatest (σ1) and least principal stress (σ3), the stress ellipsoid is characterized by an axis of intermediate principal stress (σ2), which is oriented perpendicular to the plane containing σ1 and σ3.

Each principal stress is the normal stress on horizontal or vertical plane with zero shear

Stress ellipsoid

The 3D expansion of a stress ellipse is called the stress ellipsoid.

θ is the angle between the direction of the greatest principal stress (σ1 ) and the normal (n) to the plane

STRESS EQUATIONSW

magnitudes and orientations of the principal stresses at a point are known, we can readily calculate the normal stress (σn) and shear stress (σs) for planes of any orientation using the fundamental stress equations

Types of Stress

Tension: Stress acts _|_ to and away from a plane

pulls the rock apart

forms special fractures called joint

may lead to increase in volume

Compression: stress acts _|_ to and toward a plane

Squeezes rocks

may decrease volume

Shear: acts parallel to a surface

leads to change in shape